1. Field of the Invention
The invention relates to an improved a Capacitive Micromachined Ultrasonic Transducer (CMUT) and method for manufacturing the CMUT.
2. Description of the Background Art
FIGS. 1 to 3 illustrate a conventional working principle of a Capacitive Micromachined Ultrasonic Transducer (CMUT) 100 with a flat bottom electrode 140.
Referring to FIG. 1, a CMUT 100 is similar to a parallel plate capacitor having a top electrode 110 on a dielectric membrane 120 that is isolated by a vacuum or air cavity 130 to a bottom electrode 140. The bottom electrode 140 is usually formed on a flat conductive substrate. The top electrode 110 and the bottom electrode 140 may be made from a conductive material such as a conductive silicon substrate. The membrane 120 is made from conductive material or is coated with a conductive material. When actuated by electrostatic force with an AC voltage, the membrane 120 can vibrate to generate ultrasound like a drum diaphragm. Therefore, the CMUT 100 can be used as an ultrasound emitter and receiver. Only 25% of the area near the center of the membrane 120 is patterned with a top electrode 110 since the remaining 75% area has much less capacitance change, which is considered as parasitic capacitance to be removed. In other words, only 25% of the central area of the membrane 120 is patterned with a top electrode 110 to conduct effective capacitance.
In FIG. 2, when a DC bias voltage is applied, the electrostatic force pushes the membrane 120 toward the bottom electrode 140. The effective capacitance is inversely proportional to the gap distance of the air cavity 130 between the top electrode 110 and the bottom electrode 140. In other words, effective capacitance can be achieved only when the gap distance is small. Only the middle section of membrane 120 can produce effective capacitance even if the entire membrane 120 is patterned with top electrode 110 because the bottom electrode 140 has a flat bottom. For instance, the capacitance produced in area 150 is considered parasitic capacitance.
To increase the sensitivity, the DC bias voltage is applied to load up the capacitor with charges, which can also pull the membrane 120 closer to the bottom electrode 140 to get a higher capacitance. The maximum sensitivity can be achieved when the membrane 120 is closest to the bottom electrode 140 without collapsing to the bottom electrode 140.
As the DC bias voltage increases, deflection of the membrane 120 also increases. However, when the DC bias voltage is increased above a certain voltage, electrostatic forces pressure the membrane 120 to collapse on the bottom electrode 140.
FIG. 3 illustrates a situation where the DC bias voltage is used to collapse the membrane 120. As a result, the contribution of the affected areas 160 to the effective capacitance is significantly reduced. When the DC bias voltage is large enough to bring the membrane 120 to be deflected to more than ⅓ of the gap distance of the air gap 130, the membrane 120 will collapse and make contact with the bottom electrode 140.
FIG. 4 illustrates the conventional CMUT arrays. The top electrodes 310 can only cover part of the membrane.
Referring to FIG. 5, the capacitance is simply a series combination of two parallel plate capacitors, capacitance C1 is the capacitance of dielectric membrane, and C2 is the capacitance of the air cavity, where d1 is the thickness of the membrane, d2 is the depth of the air cavity, b is the radius of the top electrode, ∈1 and ∈2 are the relative dielectric constants, ∈0 is the vacuum permittivity.
  C  =            1                        1                      C            1                          +                  1                      C            2                                =                  1                              1                                          ɛ                0                            ⁢                              ɛ                1                            ⁢                              A                                  d                  1                                                              +                      1                                          ɛ                0                            ⁢                              ɛ                2                            ⁢                              A                                  d                  2                                                                        =                                    πɛ            0                    ⁢                      b            2                                                              d              1                                      ɛ              1                                +                                    d              2                                      ɛ              2                                          
Referring to FIG. 6, for a flat bottom electrode with deflected membrane of a conventional CMUT, the deflected circular membrane is assumed to be a spherical shell partially covered by the top electrode, where Ra is the inner shell radius, Rb is the outer shell radius, and h is the height of the inner shell. C1 from the deflected dielectric membrane is calculated by the equation of parallel plate capacitor with the area of the partial spherical shell.
      C    1    =      4    ⁢                  ⁢          πɛ      0        ⁢          ɛ      1        ⁢    h    ⁢                  ⁢                            R          a                ⁢                  R          b                            d        1            
The capacitance in the air cavity between the bottom of the deflected membrane with radius Rb and the flat bottom electrode is calculated as follows.C2=(The parallel plate capacitance between the flat bottom electrode and the virtual flat plate (dashed line))−(The capacitance between the spherical shell with radius Rb and the virtual flat plate).
            C      2        =          1                        1                                    ɛ              0                        ⁢                          ɛ              2                        ⁢                                          π                ⁢                                                                  ⁢                                  b                  2                                                            d                2                                                    -                  1                      2            ⁢                                                  ⁢                          πɛ              0                        ⁢                          ɛ              2                        ⁢                          R              b                        ⁢            ln            ⁢                                                  ⁢                          H                                                                                          R                      b                      2                                        -                                          b                      2                                                                      -                                                                            R                      b                      2                                        -                                          a                      2                                                                                                                                            C          =                      1                                          1                                  C                  1                                            +                              1                                  C                  2                                                                                                  =                                    πɛ              0                                                                        d                  1                                                  4                  ⁢                                                                          ⁢                                      ɛ                    1                                    ⁢                                      hR                    a                                    ⁢                                      R                    b                                                              +                                                d                  2                                                                      ɛ                    2                                    ⁢                                      b                    2                                                              -                              1                                  2                  ⁢                                                                          ⁢                                      ɛ                    2                                    ⁢                                      R                    b                                    ⁢                  ln                  ⁢                                                                          ⁢                                      H                                                                                                                        R                            b                            2                                                    -                                                      b                            2                                                                                              -                                                                                                    R                            b                            2                                                    -                                                      a                            2                                                                                                                                                                                        where                    R        a            =                        1                      2            ⁢                                                  ⁢            H                          ⁢                  (                                    H              2                        +                          a              2                                )                      ,                  R        b            =                        R          a                +                  d          1                      ,          h      =                        R          a                -                                            R              a              2                        -                          b              2                                          
FIG. 7 is a graph of effective capacitance with respect to membrane deflection of a conventional CMUT with flat bottom electrodes. The diameter of the silicon nitride membrane is 100 μm, the thickness of the membrane is 0.2 μm, and the depth of the air cavity is 1 μm. These values are applied into the derived equations above. The relative dielectric constant of silicon nitride film is 7.5. For CMUTs with flat bottom electrodes, the capacitance change reaches its maximum of 22% when the diameter of the top electrode is 84 μm. The capacitance change drops to 9% when the top electrode fills the membrane. The maximum capacitance at the collapsed mode can only reach 0.075 pF.